To calculate the area of an irregular plot using the Trapezoidal Rule, we first need to understand the formula for this method of numerical integration. The Trapezoidal Rule is used to estimate the area under a curve by dividing the total area into trapezoids rather than rectangles.

The formula for calculating the area using the Trapezoidal Rule is:

\(A = \frac{d}{2} \times [(f_0 + f_n) + 2(f_1 + f_2 + \ldots + f_{n-1})]\)

where:

• \(A\) is the total estimated area.
• \(d\) is the distance between each set of offsets (in this case, 1 m).
• \(f_0, f_1, \ldots , f_n\) are the offsets given (2 m, 4 m, 3 m, and 5 m).

Given the offsets are 2 m, 4 m, 3 m, and 5 m, and the spacing \(d\) is 1 m, let's apply the formula:

1. Identify the values: \(f_0 = 2\), \(f_1 = 4\), \(f_2 = 3\), and \(f_3 = 5\).
2. Substitute into the formula:

\(A = \frac{1}{2} \times [(2 + 5) + 2(4 + 3)]\)

\(A = \frac{1}{2} \times [7 + 2 \times 7]\)

\(A = \frac{1}{2} \times [7 + 14]\)

\(A = \frac{1}{2} \times 21\)

\(A = 10.5 \, m^2\)

Thus, the estimated area of the irregular plot using the Trapezoidal Rule is \(10.5 \, m^2\).

The correct answer is $10.5 \, m^2$.